# Resonant frequencies in air filled closed cylinder

I want to calculate the resonant frequencies of a closed cylinder covered with rigid walls. The cylinder is of dimensions: diameter = $$1m$$, length = $$1m$$. Would this fundamental mode formula be correct to use in this case:

$$f = \frac{v_{sound}}{2L}$$

I think it is only valid for one-dimensional ducts such that diameter $$\ll$$ length but I am not sure about this. Could you please help me out with an explanation and how the above formula was derived and in which conditions is it valid to be used?

• This formula is for a cylinder open at one end. Is this your type of cylinder?
– nasu
Mar 21, 2019 at 19:51
• Yes that's right. Thank you. I have just corrected the formula. Mar 22, 2019 at 4:52

• For the OP's situation where the length = diameter, this will give only a small number of the possible resonances. For example, a rectangular box (e.g. a room) with dimensions $x \times y \times z$ has resonances $\dfrac v 2 \sqrt{\left(\dfrac i x\right)^2 + \left(\dfrac j y\right)^2 + \left(\dfrac k z\right)^2}$ for all integers $i. j, k >= 0$, where $v$ is the speed of sound. Similar formulas for a "wide" cylinder are more complicated. Jan 31, 2021 at 19:16